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In our multiverse, there are dozens - perhaps hundreds - of planet-wide cities teeming with many billions of sentients. Most of these cities were built with imported construction materials and have led to planets bulging with impossible structures. On some of the more improbable planets, entire mountain ranges have been dwarfed by city blocks. Entire planetoids have (probably) been mined out of existence to add to these cities.

Even if you added a solid five-kilometer layer of matter on top of Earth, that added layer would only increase Earth's volume by about 0.2%. The increase in mass - and therefore gravity - would be similarly insignificant, unless you used materials of ridiculous density.

On top of that, a city is nowhere near a solid, there's plenty of empty space(ie. rooms) and it's rare for buildings to exceed that height, even in very advanced settings.

All in all, even if all the matter came from outside of the planet, the average inhabitant of the planet wouldn't even notice the difference. You'd need proper equipment to measure it.

I disagree, the gravitational variations on coruscant are enormous and a great deal of mass flux regulation is done to keep planetary mass constant. Also the cities there are planet wide and several miles tall in all places.

Many planetoids containing rare elements have been mined out, but transporting material is very expensive on the interstellar scale. Instead, most city-planets obtain building material by pumping raw iron out from the core of the planet. Picture a solid block of wood, and then allowing a colony of paper wasps to build from it. The mass of the wood doesn't change, but it because less and less dense as material is moved from the solid inner wood to the outer living areas.

On a typical planet, the crust is just a thin, thin skin on the planet. Even if you have buildings that average 1km high, it's probably 6000-6500 KM to the center of the planet. So those buildings barely register on the surface.

Like others have said, most of that material is going to come from the planet itself, they're more likely to use local materials to avoid paying the high cost of mining and shipping it from somewhere else.

In the cases where the raw materials for the city is taken from other worlds, it might slightly increase the gravitational pull on the surface, but not in any noticeable way. You would need to import ridiculous amounts of mass to have even a .1g difference on a planet, and the majority of cities aren't quite that large.

If we assume a planet like Earth, a city "as massive (and dense) as" the Andes Mountains in South America looks like it might produce less than 60 milliGals (0.06 Gals, or 0.0006 m/s2 ), or ~0.00006% deviation of normal Earth gravity.

"as massive (and dense) as"

This'd assume the Andes and city were measured from the same baseline. And this also assumes the city is a local feature, roughly the same area as the mountains.

Judging by the GRACE map, a planetwide city that dwarfed "mountains" wouldn't produce a gravity anomaly perceptible to humans, though measurable. Effects of higher gravity might work their way into biology over generations.

"mountains"

Again, we'd have to qualify the mountains. The Andes and the Appalachians have very different effects on gravity, as seen in the map.

Edit: Forgot to factor in the "milli" in milliGals. Changed the effect from "perceptible" to "imperceptible."

Except for the rare cases when a planet lacks iron (which tends to be abundant on rocky planets), most planetwide cities are seeded with self-replicating mining and manufacturing equipment (generally along with a skeleton colony for managing that equipment early on) and populated as the city is built outward from the seed location. Transporting and de-orbiting large amounts of building material is prohibitively expensive when it can be easily mined. Depending on the technology level of the seeding civilization, this equipment may be very bulky (a large scale manufacturing module capable of building the pieces to construct copies of itself) all the way down to a few grams of grey goo (that is, nanomachines).

That said, even the largest of these modules has a mass that is no negligible compared to the mass of a planet (roughly one quadrillionth the mass of earth, for example) that the gravity never changes for any practical purpose.

When the Sprawl was built it did much to counteract the weight on the eastern North American Plate that was lost when the Greenland Glaciers melted. In the intermediary there were many more small fracture quakes like the one that the state of virginia experienced in the early 2010s.

The weight that is distributed on a tectonic plate does much to suppress or increase the incedence of tectonic events.

If a large amount of mass is redistributed to the middle of a plate then the small faults in the plate itself will become more active due to the strain. But a large dsitributed mass on a subducted end of a plate will often counteract the usual tectonic events. San Francisco has not had an event as big as the one they experienced in the 1980s, and that was due to the city that has grown there.

But the gravity is not effected as much. If you imagine a moon the size of Phobos, whose gravity well is miniscule (you could pole vault into orbit), the amount its mass would add to the earth (when distributed, which is the key metric), would not effect the gravity noticeably.

On city planets like corruscant the mass entering the city is closely balanced by garbage cannons firing waste "off world". Similarly there are limitations on taking mass off-planet without paying a fee to have it replaced. You'd think it wouldn't matter but when your cities are several miles tall mass flux on and off planet can become a problem.